The Foundations of Mathematics in the Theory of Sets

John P. Mayberry

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English

Cambridge University Press
27 October 2011

Mathematical logic; Set theory

Series: Encyclopedia of Mathematics and its Applications

This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.

By: John P. Mayberry
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 82
Dimensions: Height: 234mm, Width: 156mm, Spine: 23mm
Weight: 620g
ISBN: 9780521172714
ISBN 10: 0521172713
Series: Encyclopedia of Mathematics and its Applications
Pages: 446
Publication Date: 27 October 2011
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface; Part I. Preliminaries: 1. The idea of foundations of mathematics; 2. Simple arithmetic; Part II. Basic Set Theory: 3. Semantics, ontology and logic; 4. The principal axioms and definitions of set theory; Part III. Cantorian Set Theory: 5. Cantorian finitism; 6. The axiomatic method; 7. Axiomatic set theory; Part IV. Euclidean Set Theory: 8. Euclidian finitism; 9. The Euclidean theory of cardinality; 10. The theory of simply infinite systems; 11. Euclidean set theory from the Cantorian standpoint; 12. Envoi; Appendices; Bibliography; Index.

Reviews for The Foundations of Mathematics in the Theory of Sets

Review of the hardback: ' ... this book is thought-provoking ... distinctive approach to the twin issues of mathematical ontology and mathematical foundations'. Australasian Journal of Philosophy ...an invigorating call to foundational arms... Notre Dame Journal of Formal Logic ...this book is thought provoking...a distinctive approach to the twin issues of mathematical ontology and mathematical foundations... Australasian Journal of Philosophy ...I also think that it is one of the more philosophically significant books to have been written on this topic in some time. It provides much food for thought... this should certainly be acknowledged as an important piece of conceptual analysis, one which suggests interesting avenues for further exploration. Mary Tiles, Philosophia Mathematica ...a very lively book, filled with striking theses... The Bulletin of Symbolic Logic